SIAM Journal on Financial Mathematics· 2026Q1
Pricing American Options Time-Capped by a Drawdown Event in a Lévy Market
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- Q1SCImago
- 2026year
Short summary
This paper derives an explicit pricing formula for perpetual American put options that are terminated if the underlying asset price drops below a specified level, assuming the asset follows a geometric Lévy process with exponentially distributed downward jumps.
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Key points
- Derives an explicit price for perpetual American put options time-capped by a drawdown event.
- The underlying asset follows a geometric Lévy process with exponentially distributed downward jumps.
- The optimal exercise strategy is to stop the option when the asset price falls below a specific threshold.
- The proof combines martingale techniques with fluctuation theory for Lévy processes.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract. This paper presents a derivation of the explicit price for the perpetual American put option time-capped by the first drawdown time beyond a predefined level. The underlying asset price follows a geometric Lévy process with downward exponentially distributed jumps. We show that the optimal exercise strategy is to stop the first time the asset price falls below a certain threshold. The proof combines martingale techniques with fluctuation theory for Lévy processes. A numerical study illustrating the main results is also provided.
The authors' abstract, as published at the source. SIAM Journal on Financial Mathematics, 2026 · DOI ↗
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Field: Finance
FinanceEconomics, Econometrics and Finance